Question

The first, second and fifth terms of an arithmetic sequence are the first three consecutive terms of a geometric sequence. Find the common ratio

Answer 1

a, a+d, a+ 4d
a + ^d/_a =  ^{a + 4d}/_a+d
a(a + 4d) = (a+d)²
a² + 4ad = a² +2ad+d²
2ad = d²
2a=d
common ratio (r)
^a+2d/_a = ^a+2a/_a
=^3a/_a =3